Provides a detailed overview of stochastic control theory
Largely self-contained, allowing readers to pursue independent study
Includes several explicitly worked-out examples, helping readers to easily
understand the theory discussed
This book gathers the most essential results, including recent ones, on linear-quadratic optimal
control problems, which represent an important aspect of stochastic control. The results are
introduced in the context of finite and infinite horizon problems, and for two-player zero-sum
and nonzero-sum differential games. A number of new and interesting issues are presented,
and the interconnections between three well-known relevant issues - the existence of optimal
controls, solvability of the optimality system, and solvability of the associated Riccati equation -
are precisely identified for the first time.Though the content is largely self-contained, readers
should have a basic grasp of linear algebra, functional analysis, and stochastic ordinary
differential equations.The book is mainly intended for senior undergraduate and graduate
students majoringin applied mathematics, who are interested in stochastic control theory.
Researchers in some other related areas, such as engineering, management, finance/economics
and the social sciences, will also find the book useful.
ISBN 978-3-030-20921-6
Due 2019-09-06
1st ed. 2019, IV, 286 p. 8 illus.
Softcover
ISBN 978-3-030-21791-4
Provides an overview of the whole subject of representation theory of finite groups
A unique survey of current research aimed at beginning researchers
Only basic knowledge is assumed with most topics covered in a self-contained fashion
This book provides an accessible introduction to the state of the art of representation theory of
finite groups. Starting from a basic level that is summarized at the start, the book proceeds to
cover topics of current research interest, including open problems and conjectures. The central
themes of the book are block theory and module theory of group representations, which are
comprehensively surveyed with a full bibliography. The individual chapters cover a range of
topics within the subject, from blocks with cyclic defect groups to representations of symmetric
groups. Assuming only modest background knowledge at the level of a first graduate course in
algebra, this guidebook, intended for students taking first steps in the field, will also provide a
reference for more experienced researchers. Although no proofs are included, end-of-chapter
exercises make it suitable for student seminars.
Due 2019-09-07
3rd ed. 2019, X, 566 p. 239
illus., 33 illus. in color.
Hardcover
ISBN 978-3-030-21472-2
Engineering Use of Group-Theoretic Bifurcation Theory
Exercises at the ends of chapters or sections
Solutions to selected exercises in the book
Detailed Illustrations
This book provides a modern static imperfect bifurcation theory applicable to bifurcation
phenomena of physical and engineering problems and fills the gap between the mathematical
theory and engineering practice. Systematic methods based on asymptotic, probabilistic, and
group theoretic standpoints are used to examine experimental and computational data from
numerous examples, such as soil, sand, kaolin, honeycomb, and domes. For mathematicians,
static bifurcation theory for finite-dimensional systems, as well as its applications for practical
problems, is illuminated by numerous examples. Engineers may find this book, with its
minimized mathematical formalism, to be a useful introduction to modern bifurcation theory.
This third edition strengthens group representation and group-theoretic bifurcation theory.
Several large scale applications have been included in association with the progress of
computational powers. Problems and answers have been provided. Review of First Edition: "The
book is unique in considering the experimental identification of material-dependent bifurcations
in structures such as sand, Kaolin (clay), soil and concrete shells. … These are studied
statistically. … The book is an excellent source of practical applications for mathematicians
working in this field. … A short set of exercises at the end of each chapter makes the book
more useful as a text. The book is well organized and quite readable for non-specialists." Henry
W. Haslach, Jr., Mathematical Reviews, 2003
Due 2019-09-11
1st ed. 2019, VIII, 252 p.
17 illus., 11 illus. in color.
Hardcover
ISBN 978-3-030-22284-0
Pays attention to the interaction of the both research areas on backward
stochastic differential equations (BSDEs) and on stochastic partial differential
equations (SPDEs)
Provides new insights and approaches
Written by experts in the field
This collection of selected, revised and extended contributions resulted from a Workshop on
BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and
included the 8th World Symposium on BSDEs. The volume addresses recent advances involving
backward stochastic differential equations (BSDEs) and stochastic partial differential equations
(SPDEs). These equations are of fundamental importance in modelling of biological, physical
and economic systems, and underpin many problems in control of random systems,
mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek
to understand these equations, and to use them to build our understanding in other areas of
mathematics. This volume will be of interest to those working at the forefront of modern
probability theory, both established researchers and graduate students.
Due 2019-09-29
1st ed. 2019, VI, 469 p. 19
illus., 10 illus. in color.
Hardcover
ISBN 978-3-030-23530-7
Commemorates the mathematical achievements of Anthony Joseph, one of Lie
theory’s leading figures
Explores recent advances in topics that Joseph fundamentally influenced
Equips readers with an understanding of various subjects within Lie algebra
and representation theory
This volume, a celebration of Anthony Joseph’s fundamental influence on classical and
quantized representation theory, explores a wide array of current topics in Lie theory by experts
in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of
Representations,” the first of which was held from July 16-18 at the Weizmann Institute of
Science and the second from July 19-23 at the University of Haifa. The chapters in this volume
cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group
actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is
addressed to mathematicians who specialize in representation theory and Lie theory, and who
wish to learn more about this fascinating subject.
Due 2019-09-10
1st ed. 2019, VIII, 470 p. 8 illus.
Hardcover
ISBN 978-3-030-22421-9
First book in decades to discuss a variety of proofs of Loewner's Theorem
May be used as a text for a specialized graduate analysis course
Acts as a starting point for discussing a variety of methods in analysis
This book provides an in depth discussion of Loewner’s theorem on the characterization of
matrix monotone functions. The author refers to the book as a ‘love poem,’ one that highlights
a unique mix of algebra and analysis and touches on numerous methods and results. The
book details many different topics from analysis, operator theory and algebra, such as divided
differences, convexity, positive definiteness, integral representations of function classes, Pick
interpolation, rational approximation, orthogonal polynomials, continued fractions, and more.
Most applications of Loewner’s theorem involve the easy half of the theorem. A great number
of interesting techniques in analysis are the bases for a proof of the hard half. Centered on
one theorem, eleven proofs are discussed, both for the study of their own approach to the
proof and as a starting point for discussing a variety of tools in analysis. Historical background
and inclusion of pictures of some of the main figures who have developed the subject, adds
another depth of perspective. The presentation is suitable for detailed study, for quick review or
reference to the various methods that are presented. The book is also suitable for independent
study. The volume will be of interest to research mathematicians, physicists, and graduate
students working in matrix theory and approximation, as well as to analysts and mathematical
physicists